Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
from sys import stdin

t=[(x*(x+1)//2) for x in range(44730)]
num = int(stdin.readline().strip())


i,found = 1,False
for y in range(len(t)):
    if 2*t[y]==num:
        found=True
        
while found==False and t[i]<num:
    target = num-t[i]
    low,hi = i,44730
    while found==False and low+1<hi:
        mid = low+((hi-low)//2)
        if t[mid]==target:
            found = True
        elif t[mid]<target:
            low = mid
        else:
            hi = mid
    i += 1
if found:
    print("YES")
else:
    print("NO")